Abstract: A subset of blazars emit TeV gamma rays which annihilate and pair produce on
the extragalactic background light. We have argued in Broderick et al. (2011,
Paper I) that plasma beam instabilities can dissipate the pairs' energy
locally. This heats the intergalactic medium and dramatically increases its
entropy after redshift z~2, with important implications for structure
formation: (1) This suggests a scenario for the origin of the cool core
(CC)/non-cool core (NCC) bimodality in galaxy clusters and groups. Early
forming galaxy groups are unaffected because they can efficiently radiate the
additional entropy, developing a CC. However, late forming groups do not have
sufficient time to cool before the entropy is gravitationally reprocessed
through successive mergers - counteracting cooling and raising the core entropy
further. Hence blazar heating works different than feedback by active galactic
nuclei, which balances radiative cooling but is unable to transform CC into NCC
clusters due to the weak coupling to the cluster gas. (2) We predict a
suppression of the Sunyaev-Zel'dovich power spectrum on angular scales smaller
than 5' due to the globally reduced central pressure of groups and clusters
forming after z~1. (3) Our redshift dependent entropy floor increases the
characteristic halo mass below which dwarf galaxies cannot form by a factor of
~10 (50) at mean density (in voids) over that found in models that include
photoionization alone. This prevents the formation of late forming dwarf
galaxies (z<2) with masses ranging from 10^{10} to 10^{11} M_sun for redshifts
z~2 to 0, respectively. This may help resolve the "missing satellite problem"
in the Milky Way and the "void phenomenon" of the low observed abundances of
dwarf satellites compared to cold dark matter simulations and may bring the
observed early star formation histories into agreement with galaxy formation
models. (abridged)